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Single Idea 19305

[filed under theme 10. Modality / B. Possibility / 6. Probability ]

Full Idea

The Gambler's Fallacy says if black has come up ten times in a row, red must be highly probable next time. It overlooks how the impact of an initial run of one color can become more and more insignificant as the sequence gets longer.

Gist of Idea

The Gambler's Fallacy (ten blacks, so red is due) overemphasises the early part of a sequence

Source

Gilbert Harman (Change in View: Principles of Reasoning [1986], 1)

Book Ref

Harman,Gilbert: 'Change in View: Principles of Reasoning' [MIP 1986], p.8

A Reaction

At what point do you decide that the roulette wheel is fixed, rather than that you have fallen for the Gambler's Fallacy? Interestingly, standard induction points to the opposite conclusion. But then you have prior knowledge of the wheel.

The 15 ideas with the same theme [asserting the degree of likelihood of a fact]:

2216 We transfer the frequency of past observations to our future predictions [Hume]
19142 Probability can be constrained by axioms, but that leaves open its truth nature [Davidson]
19305 The Gambler's Fallacy (ten blacks, so red is due) overemphasises the early part of a sequence [Harman]
19310 High probability premises need not imply high probability conclusions [Harman]
7448 Probability is statistical (behaviour of chance devices) or epistemological (belief based on evidence) [Hacking]
7447 Probability was fully explained between 1654 and 1812 [Hacking]
7449 Epistemological probability based either on logical implications or coherent judgments [Hacking]
14281 A thing works like formal probability if all the options sum to 100% [Edgington]
14284 Conclusion improbability can't exceed summed premise improbability in valid arguments [Edgington]
13857 Truth-functional possibilities include the irrelevant, which is a mistake [Edgington]
6796 Subjective probability measures personal beliefs; objective probability measures the chance of an event happening [Bird]
6797 Objective probability of tails measures the bias of the coin, not our beliefs about it [Bird]
14903 Quantum mechanics seems to imply single-case probabilities [Ladyman/Ross]
14923 In quantum statistics, two separate classical states of affairs are treated as one [Ladyman/Ross]
24054 Everything has a probability, something will happen, and probabilities add up [PG]